Energy, work and power
Work and energy
- Work done by a constant force: $W = Fd\cos\theta$ (measured in joules).
- Kinetic energy (movement): $\text{KE} = \tfrac12 mv^2$.
- Gravitational potential energy (height): $\text{PE} = mgh$.
- With no friction, total energy is conserved (conservation of energy).
Practice
What is the kinetic energy of a 2 kg object moving at 3 m/s (KE = ½mv²), in J?
KE = ½ × 2 × 3² = ½ × 2 × 9 = 9 J.
Practice
Taking g = 10, what is the PE of a 2 kg object raised 5 m (PE = mgh), in J?
PE = mgh = 2 × 10 × 5 = 100 J.
Power
- Power is the rate of doing work (in watts).
- For a force pulling along the motion: $P = Fv$.
- Example: $P = 12\,\text{kW}$ at $v = 20\,\text{m s}^{-1}$ → driving force $F = \dfrac{12000}{20} = 600\,\text{N}$.
Practice
A car works at 12 kW at 20 m/s. Using P = Fv, what is the driving force, in N?
F = P/v = 12000/20 = 600 N.
You've got it
Key idea
- work $W = Fd\cos\theta$; KE $= \tfrac12 mv^2$; PE $= mgh$
- with no friction, total energy is conserved
- power = rate of work; $P = Fv$